Estimating division that results in non whole numbers

So let's think about something a little bit. What do you think 17 divided by 2 is going to be? Well, you might immediately realize that it's not obvious what you need to multiply 2 by in order to get to 17. There's no whole number that I could put here that gets us to 17.

We know that 2 times... let's see, 2 times 8 is a little bit less than that. 2 times 8 is equal to 16, and we know that 2 times 9 is going to be a little bit more than that, is equal to 18.

And so, this question mark, 2 times question mark is equal to 17. This helps us know that our question mark, our unknown value here, is going to be between 8 and 9. It is going to be 8 point something.

So let's do another example. If someone were to ask you, hey, let's think about 18 divided by 4, and you don't have to figure out exactly what it is just yet, but I want you to think about what two consecutive whole numbers is 18 divided by 4. Whatever that is, what is that between?

Well, we could do something similar. We could say, all right, let's see, 4 times 4 is equal to 16, so that doesn't quite get us to 18. We could say that 4 times 5 is equal to 20, so that's more than 18.

So 4 times question mark is equal to 18. This helps us realize that because 18 is between 16 and 20, this question mark right over here is going to be between 4 and 5. So 18 divided by 4 is going to be 4 point something.

Now, another way of thinking about or estimating what division might result in is through an inequality. So if I were to say 87 divided by 9, how would you compare that to 10 over here?

So there's a couple of ways you could compare it. You could say maybe this is greater than 10, maybe it's equal to 10, maybe it is less than ten. So pause this video and see if you can figure that out. What would you put here? Is it less than, greater than, or equal to ten?

Well, we know it's not equal to ten. We know that ninety divided by nine is equal to ten. And let's see if we go one multiple of nine less than that, we know that 81 divided by nine is equal to nine.

And so 87 divided by nine is in between these two values. Let me do this in another color. So 87 divided by nine is going to be something in between nine and ten, and so it is going to be less than ten.

So the whole point of this video is to start to get us a little bit comfortable with this idea of dividing where we might get an answer that is not a whole number. In the future, we'll learn how to compute that, but for now, we're just learning to estimate and just get a sense of, hey, okay, this is going to be between eight and nine, this is going to be between four and five, this is going to be between nine and ten, which just means it's going to be nine point something, which means it's going to be less than ten.